A small drip at a bathroom faucet may come from the aerator, cartridge, or a loose connection. Checking the aerator is a simple first step that can remove mineral debris without replacing the whole faucet.
Protect the drain
Close the drain or place a cloth over it before removing small parts. Turn off the faucet and dry the area.
Remove the aerator gently
Wrap the aerator with cloth before using pliers. Keep the pieces in order and note the screen orientation.
Clean and inspect
Rinse grit and soak mineral deposits with an approved method. Replace a damaged screen or washer, then reinstall by hand.
Test the source
Run the faucet and observe the spout and handle. If dripping continues with the faucet closed, the internal cartridge may need service.